427 research outputs found
Optimal Co-linear Gaussian Beams for Spontaneous Parametric Down-Conversion
I investigate the properties of spontaneous parametric down-conversion (SPDC)
involving co-linear Gaussian spatial modes for the pump and the photon
collection optics. Approximate analytical and numerical results are obtained
for the peak spectral density, photon bandwidth, pair collection probability,
heralding ratio, and spectral purity, as a function of crystal length and beam
focusing parameters. I address the optimization of these properties
individually as well as jointly, and find focusing conditions that
simultaneously bring the pair collection probability, heralding ratio, and
spectral purity to near-optimal values. These properties are also found to be
nearly scale invariant, that is, ultimately independent of crystal length. The
results obtained here are expected to be useful for designing SPDC sources with
high performance in multiple categories for the next generation of SPDC
applications.Comment: 15 pages, 8 figures. Corrected normalization coefficient in eqn. 1
and a typo in the definition of wavenumber following eqn. 7. No results were
affected by these correction
Counting Abelian Squares for a Problem in Quantum Computing
In a recent work I developed a formula for efficiently calculating the number
of abelian squares of length over an alphabet of size , where may
be very large. Here I show how the expressiveness of a certain class of
parameterized quantum circuits can be reduced to the problem of counting
abelian squares over a large alphabet, and use the recently developed formula
to efficiently calculate this quantity
Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission
We present results of a bright polarization-entangled photon source operating
at 1552 nm via type-II collinear degenerate spontaneous parametric
down-conversion in a periodically poled potassium titanyl phosphate crystal. We
report a conservative inferred pair generation rate of 123,000 pairs/s/mW into
collection modes. Minimization of spectral and spatial entanglement was
achieved by group velocity matching the pump, signal and idler modes and
through properly focusing the pump beam. By utilizing a pair of calcite beam
displacers, we are able to overlap photons from adjacent down-conversion
processes to obtain polarization-entanglement visibility of 94.7 +/- 1.1% with
accidentals subtracted.Comment: 4 pages, 7 color figures. Revised manuscript includes the following
changes: corrected pair generation rate from 44,000/s/mW pump to 123,000/s/mW
pump; replaced Fig. 1b to enhance clarity; minor alterations to the title,
abstract and introduction; grammatical correction
Variational quantum regression algorithm with encoded data structure
Variational quantum algorithms (VQAs) prevail to solve practical problems
such as combinatorial optimization, quantum chemistry simulation, quantum
machine learning, and quantum error correction on noisy quantum computers. For
variational quantum machine learning, a variational algorithm with model
interpretability built into the algorithm is yet to be exploited. In this
paper, we construct a quantum regression algorithm and identify the direct
relation of variational parameters to learned regression coefficients, while
employing a circuit that directly encodes the data in quantum amplitudes
reflecting the structure of the classical data table. The algorithm is
particularly suitable for well-connected qubits. With compressed encoding and
digital-analog gate operation, the run time complexity is logarithmically more
advantageous than that for digital 2-local gate native hardware with the number
of data entries encoded, a decent improvement in noisy intermediate-scale
quantum computers and a minor improvement for large-scale quantum computing Our
suggested method of compressed binary encoding offers a remarkable reduction in
the number of physical qubits needed when compared to the traditional
one-hot-encoding technique with the same input data. The algorithm inherently
performs linear regression but can also be used easily for nonlinear regression
by building nonlinear features into the training data. In terms of measured
cost function which distinguishes a good model from a poor one for model
training, it will be effective only when the number of features is much less
than the number of records for the encoded data structure to be observable. To
echo this finding and mitigate hardware noise in practice, the ensemble model
training from the quantum regression model learning with important feature
selection from regularization is incorporated and illustrated numerically
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